I tried looking this up and I saw a lot of mention of "JOINS," but I'm not that experienced with SQL. So I was wondering: would my solution logically work? and how is it different from a JOIN where you actually use the JOIN keyword?

Yes, what you did will work and that is actually what we call an "Equijoin."
However, if you work on a lot of tables it is more efficient to explicitly use join syntax as Barmar pointed out with regard to readability of code.